Resources tagged with: Proof by contradiction

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There are 12 NRICH Mathematical resources connected to Proof by contradiction, you may find related items under Thinking Mathematically.

Broad Topics > Thinking Mathematically > Proof by contradiction

Eyes Down

Age 16 to 18
Challenge Level

The symbol [ ] means 'the integer part of'. Can the numbers [2x]; 2[x]; [x + 1/2] + [x - 1/2] ever be equal? Can they ever take three different values?

Mastering Mathematics: the Challenge of Generalising and Proof

Age 5 to 11

This article for primary teachers discusses how we can help learners generalise and prove, using NRICH tasks as examples.

Impossible Square?

Age 16 to 18
Challenge Level

Can you make a square from these triangles?

Rarity

Age 16 to 18
Challenge Level

Show that it is rare for a ratio of ratios to be rational.

An Introduction to Proof by Contradiction

Age 14 to 18

An introduction to proof by contradiction, a powerful method of mathematical proof.

The Dangerous Ratio

Age 11 to 14

This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying.

Rational Round

Age 16 to 18
Challenge Level

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.

Proof Sorter - the Square Root of 2 Is Irrational

Age 16 to 18
Challenge Level

Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.

Staircase

Age 16 to 18
Challenge Level

Solving the equation x^3 = 3 is easy but what about solving equations with a 'staircase' of powers?

Tetra Inequalities

Age 16 to 18
Challenge Level

Prove that in every tetrahedron there is a vertex such that the three edges meeting there have lengths which could be the sides of a triangle.

Proximity

Age 14 to 16
Challenge Level

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

Be Reasonable

Age 16 to 18
Challenge Level

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.